Abstract:"Static" spherically symmetric perfect fluid solutions in General Relativity can be exhaustively classified. The physical interpretations of the resulting four classes, one being new, are different from each other. Some of the "solutions" look naively like black hole spacetimes and sometimes are presented as such. But these solutions make transitions between the classes mentioned, hence are not "simple". It is concluded that no "simple" black hole solutions exist beyond those already known (Schwarzschild and Schwarzschild-de Sitter) .